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[null,"     Visualizing the Quotient Rule"]
[]
[null,"    This DIGMath program helps you visualize "]
[null,"      the Quotient Rule for finding the derivative"]
[null,"     of the quotient f(x)/g(x) of two functions:  "]
[null,null,"       y = f(x)    and    y = g(x)"]
[null,"          on any interval from x = a  to x = b."]
[]
[]
["Enter the first function in terms of x:   y = f(x) =  ",{"$nulls":4},"sin(3*x)"]
[]
["Enter the second function in terms of x:  y = g(x) = ",{"$nulls":4},"x^3"]
[]
[{"$nulls":8},"Now trace along the various curves:"]
["Now enter the interval for x :  ",{"$nulls":7},"x  = ",{"$f":"D16+K15*Sheet2!B12","v":1.3317365269461077},315]
[null,"   Starting value a =",null,0.2,{"$nulls":4},"f(x) =",{"$f":"LOOKUP(J15,Sheet2!C3:C504,Sheet2!D3:D504)","v":-0.7465347002785719},null,"        slope of  f(x) =",{"$f":"LOOKUP(x0,Sheet2!C3:C504,Sheet2!E3:E504)","v":-1.9839311924992915}]
[null,"    Ending value b =",null,2,{"$nulls":4},"g(x) =",{"$f":"LOOKUP(J15,Sheet2!C$3:C$504,Sheet2!F$3:F$504)","v":2.3427999818785756},null,"        slope of g(x) =",{"$f":"LOOKUP(x0,Sheet2!C3:C504,Sheet2!G3:G504)","v":5.306225393524542}]
[{"$nulls":8},"f(x)/g(x) =",{"$f":"LOOKUP(x0,Sheet2!C$3:C$504,Sheet2!H$3:H$504)","v":-0.31865063430637497},null,"slope of quotient f/g is",{"$f":"LOOKUP(x0,Sheet2!C3:C504,Sheet2!I3:I504)","v":{"v":-0.12409650692338754,"d":"-0.12"}}]
[]
[{"$nulls":8},"f'(x)/g'(x) =",{"$f":"LOOKUP(x0,Sheet2!C$3:C$504,Sheet2!J$3:J$504)","v":{"v":-0.3738874709167809,"d":"-0.37"}},null,"[f '(x)g(x) - f(x)g'(x)]/g2(x) =",{"$f":"LOOKUP(x0,Sheet2!C$3:C$504,Sheet2!K$3:K$504)","v":0.12510632890012235}]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[null,null,"   Item 4"]
[]
[]
[]
["To access/download all the DIGMath Apps for Calculus"]
["     Click this link:",null,"DIGMath for Calculus"]
[]
["Created by:  Sheldon P. Gordon   "]
["                      Farmingdale State College    "]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

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